# How do you find the product (4x+5)(4x+5)?

Jun 15, 2018

See a solution process below:

#### Explanation:

This problem can be rewritten as:

What is: ${\left(4 x + 5\right)}^{2}$

This is a special form of the quadratic which can be expanded using the rule:

${\left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right)}^{2} = \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) = {\textcolor{red}{x}}^{2} + 2 \textcolor{red}{x} \textcolor{b l u e}{y} + {\textcolor{b l u e}{y}}^{2}$

Substitute $\textcolor{red}{4 x}$ for $\textcolor{red}{x}$ and $\textcolor{b l u e}{5}$ for $\textcolor{b l u e}{y}$ gives:

${\left(\textcolor{red}{4} + \textcolor{b l u e}{5}\right)}^{2} = \left(\textcolor{red}{4} + \textcolor{b l u e}{5}\right) \left(\textcolor{red}{4} + \textcolor{b l u e}{5}\right) = {\left(\textcolor{red}{4 x}\right)}^{2} + \left(2 \cdot \textcolor{red}{4 x} \cdot \textcolor{b l u e}{5}\right) + {\textcolor{b l u e}{5}}^{2} = 16 {x}^{2} + 40 x + 25$